Simplify Square Root of 24768

Here we will show you two methods that you can use to simplify the square root of 24768. In other words, we will show you how to find the square root of 24768 in its simplest radical form using two different methods.

To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√24768 = A√B

Greatest Perfect Square Factor Method
The Greatest Perfect Square Factor Method uses the greatest perfect square factor of 24768 to simplify the square root of 24768. This is how to calculate A and B using this method:

A = Calculate the square root of the greatest perfect square from the list of all factors of 24768. The factors of 24768 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 43, 48, 64, 72, 86, 96, 129, 144, 172, 192, 258, 288, 344, 387, 516, 576, 688, 774, 1032, 1376, 1548, 2064, 2752, 3096, 4128, 6192, 8256, 12384, and 24768. Furthermore, the greatest perfect square on this list is 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Calculate 24768 divided by the greatest perfect square from the list of all factors of 24768. We determined above that the greatest perfect square from the list of all factors of 24768 is 576. Furthermore, 24768 divided by 576 is 43, therefore B equals 43.

Now we have A and B and can get our answer to 24768 in its simplest radical form as follows:

√24768 = A√B

√24768 = 24√43

Double Prime Factor Method
The Double Prime Factor Method uses the prime factors of 24768 to simplify the square root of 24768 to its simplest form possible. This is how to calculate A and B using this method:

A = Multiply all the double prime factors (pairs) of 24768 and then take the square root of that product. The prime factors that multiply together to make 24768 are 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 43. When we strip out the pairs only, we get 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576 and the square root of 576 is 24. Therefore, A equals 24.

B = Divide 24768 by the number (A) squared. 24 squared is 576 and 24768 divided by 576 is 43. Therefore, B equals 43.

Once again we have A and B and can get our answer to 24768 in its simplest radical form as follows:

√24768 = A√B

√24768 = 24√43

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